Moore plane

There are closed quotients of the Moore plane which provide counterexamples.

The Moore plane is not locally compact.

Thus, the Moore plane shows that a subspace of a separable space need not be separable.

An easy example of a non-metacompact space (but a countably metacompact space) is the Moore plane.

The Moore plane is separable, that is, it has a countable dense subset.

The Moore plane is first countable, but not second countable or Lindelöf.

The Moore plane (also known as the Niemytski space) is an example of a non-metrizable Moore space.

The Moore plane is a completely regular Hausdorff space (i.e. Tychonoff space), which is not normal.

The Moore plane, Moore's road space, Moore space and the Moore space conjecture are named in his honour.

In mathematics, the Moore plane, also sometimes called Niemytzki plane (or Nemytskii plane, Nemytskii's tangent disk topology) is a topological space.